Numerical simulations of Plano-Taylor-Couette flow

The plane-Couette flow and the Taylor-Couette flow are two classical fluid dynamical systems that have been studied in great detail. However, the mechanism of how these two canonical flows may interact remains unexplored. Here we use a numerical method to simulate a flow geometry formed between sliding conveyor belts, which combines a linear, plane-Couette region and a curved, Taylor-Couette region. The geometry is mainly defined by the parameters L / r_i and (r_o-r_i) / r_i, where r_o, r_i are the outer and inner radius of Taylor-Couette region, and L is the length of linear plane-Couette region. When L << r_i, this system reaches the limit of the Taylor-Couette flow, while in the limit L >> r_i the plane-Couette geometry is dominant. We explore the situation where the outer belt is fixed and only the inner one is moving, and quantify the torque and drag for varying L / r_i. We draw insights about how the flow transitions from one limit to the other, with changing L / r_i, and within the merging zone.